CN112711980A - Method for selecting wavelet base in mineral spectral feature extraction - Google Patents
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Abstract
The invention belongs to the technical field of spectral signal processing and hyperspectral mineral mapping, and particularly relates to a method for selecting a wavelet basis in mineral spectral feature extraction, which comprises the following steps: step one, acquiring mineral spectrum data; secondly, denoising the mineral spectrum in the first step by a mean value method; determining the category of the wavelet cluster to be selected and a series of wavelet bases contained in the wavelet cluster to be selected; step four, performing multi-scale one-dimensional discrete wavelet decomposition on the mineral spectrum signals in the step two by using the wavelet basis in the step three to obtain high-frequency detail coefficients and low-frequency approximate coefficients of different scales; step five, performing soft threshold processing on all the high-frequency detail coefficients obtained in the step four; step six, obtaining a reconstructed signal after the soft threshold value noise reduction; step seven, calculating the correlation coefficient of the reconstructed signal in the step six and the mineral spectrum original signal in the step two; step eight, determining a wavelet basis corresponding to the maximum correlation coefficient in the step seven; and step nine, extracting spectral characteristics of minerals.
Description
Technical Field
The invention belongs to the technical field of spectral signal processing and hyperspectral mineral mapping, and particularly relates to a method for selecting wavelet bases in mineral spectral feature extraction.
Background
Different types of ground objects have unique spectral characteristics, and the mineral type and the mineral component can be directly identified according to the diagnostic spectral characteristics of minerals. However, the hyperspectral data has large information amount and long processing time, effective spectral features are screened and extracted from the hyperspectral data, the classification performance can be enhanced, and the processing efficiency is obviously improved on the premise of ensuring the precision.
The wavelet transform has the capability of representing the local characteristics of the signals in the time domain and the frequency domain, can analyze the characteristics of the signals from the transform results of the signals under different scales, and is widely applied in the field of signal processing. However, different wavelet bases have different time-frequency characteristics, the waveform difference is large, and the support length and the regularity are different.
Therefore, different wavelet bases are selected for the same mineral spectrum signal to be processed, the obtained results are often very different, and how to select the optimal wavelet base for extracting the mineral spectrum feature is a problem which needs to be intensively solved at present.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for selecting wavelet bases in mineral spectral feature extraction, which is used for solving the technical problem of how to select the optimal wavelet bases for mineral spectral feature extraction.
The technical scheme of the invention is as follows:
a method for selecting wavelet base in mineral spectral feature extraction comprises the following steps:
step one, acquiring mineral spectrum data;
secondly, denoising the mineral spectrum in the first step by a mean value method;
determining the category of the wavelet cluster to be selected and a series of wavelet bases contained in the wavelet cluster to be selected;
step four, performing multi-scale one-dimensional discrete wavelet decomposition on the mineral spectrum signals in the step two by using the wavelet basis in the step three to obtain high-frequency detail coefficients and low-frequency approximate coefficients of different scales;
step five, performing soft threshold processing on all the high-frequency detail coefficients obtained in the step four;
step six, performing wavelet reconstruction by using the high-frequency detail coefficient of each scale processed by the soft threshold in the step five and the highest-scale low-frequency approximate coefficient obtained in the step four to obtain a reconstructed signal subjected to soft threshold noise reduction;
step seven, calculating the correlation coefficient of the reconstructed signal in the step six and the mineral spectrum original signal in the step two;
step eight, determining a wavelet basis corresponding to the maximum correlation coefficient in the step seven;
and step nine, performing wavelet transformation on the spectral signal to be detected by using the wavelet basis determined in the step eight, and extracting the mineral spectral characteristics.
The first step further comprises: the measured spectrum curve of a certain mineral is recorded as Xi(lambda), wherein lambda is the serial number of the spectral band, and i is the serial number of the mineral spectrum measured multiple times.
The second step further comprises: de-noising the mineral spectrum in the first step by a mean value method, and measuring a certain mineral spectrum curve Xi(lambda), summing according to corresponding wave bands, and then taking an average value, and recording the result as Z (lambda); assuming that n spectral measurements are performed on the mineral, the formula of mean denoising is as follows (1):
the fourth step further comprises: the wavelet basis functions are noted
Using wavelet bases
For mineral spectral signal Z (lambda)Performing m-layer one-dimensional discrete wavelet decomposition to obtain high-frequency detail coefficients D with different scalesi(i ═ 1,2, …, m) and low frequency approximation coefficient ai(i＝1,2,…,m)。
The fifth step further comprises: all the high-frequency detail coefficients D obtained in the step fouri(i 1,2, …, m) was soft thresholded, the result being denoted as Di'(i＝1,2,…,m)。
The sixth step further comprises: utilizing the high-frequency detail coefficient D of each scale after the five soft threshold processing of the stepsi' (i is 1,2, …, m) and the highest scale low frequency approximation coefficient A obtained in step fourmAnd performing wavelet reconstruction to obtain a reconstructed signal S (lambda) subjected to soft threshold denoising.
The seventh step further comprises: and (3) calculating a correlation coefficient CC of the reconstructed signal S (lambda) in the sixth step and the original mineral spectrum signal Z (lambda) in the second step, wherein the calculation formula is as follows (2):
wherein cov represents a covariance operation.
The eighth step further comprises: and sequencing the correlation coefficients CC calculated in the seventh step, and marking the wavelet basis corresponding to the maximum CC as sigma.
The invention has the beneficial effects that:
the invention carries out multi-scale one-dimensional discrete wavelet decomposition on mineral spectrum signals by selecting a series of wavelet bases in different wavelet clusters, carries out wavelet reconstruction by utilizing each scale high-frequency detail coefficient and the highest scale low-frequency approximate coefficient after soft threshold processing, and calculates the correlation coefficient of the reconstructed signals and the original signals as the selection criterion of the optimal wavelet base for extracting the mineral spectrum characteristics.
The method is simple, convenient and quick, realizes quick selection of the optimal wavelet base, improves the effect of extracting the spectral characteristics of the mineral and the efficiency of signal processing, reduces the interference of human experience, and has wide application range.
Detailed Description
The technical solution of the present invention is further described with reference to the accompanying drawings and specific embodiments,
as shown in FIG. 1, the method for selecting wavelet basis in mineral spectral feature extraction designed by the invention specifically comprises the following steps:
step one, acquiring mineral spectrum data; the measured spectrum curve of a certain mineral is recorded as Xi(lambda), wherein lambda is the serial number of the spectral band, and i is the serial number of the multi-measurement mineral spectrum;
secondly, denoising the mineral spectrum in the first step by a mean value method; for certain mineral spectral curve X obtained by measurementi(lambda), summing according to corresponding wave bands, and then taking an average value, and recording the result as Z (lambda); assuming that n spectral measurements are performed on the mineral, the formula of mean denoising is as follows (1):
determining the category of the wavelet cluster to be selected and a series of wavelet bases contained in the wavelet cluster to be selected;
step four, performing multi-scale one-dimensional discrete wavelet decomposition on the mineral spectrum signals in the step two by using the wavelet basis in the step three to obtain high-frequency detail coefficients and low-frequency approximate coefficients of different scales; the wavelet basis functions are noted
Using wavelet bases
Performing m-layer one-dimensional discrete wavelet decomposition on the mineral spectrum signal Z (lambda) to obtain high-frequency detail coefficients D with different scalesi(i ═ 1,2, …, m) and low frequency approximation coefficient ai(i＝1,2,…,m)。
Step five, all the high-frequency detail coefficients D obtained in the step four are processedi(i 1,2, …, m) was soft thresholded, the result being denoted as Di'(i＝1,2,…,m)。
Step six, performing wavelet reconstruction by using the high-frequency detail coefficient of each scale processed by the soft threshold in the step five and the highest-scale low-frequency approximate coefficient obtained in the step four to obtain a reconstructed signal subjected to soft threshold noise reduction;
utilizing the high-frequency detail coefficient D of each scale after the five soft threshold processing of the stepsi' (i is 1,2, …, m) and the highest scale low frequency approximation coefficient A obtained in step fourmAnd performing wavelet reconstruction to obtain a reconstructed signal S (lambda) subjected to soft threshold denoising.
Step seven, calculating a correlation coefficient CC between the reconstructed signal S (lambda) in the step six and the original mineral spectrum signal Z (lambda) in the step two, wherein the calculation formula is as the following formula (2):
wherein cov represents a covariance operation.
Step eight, determining a wavelet basis corresponding to the maximum correlation coefficient in the step seven; and sequencing the correlation coefficients CC calculated in the seventh step, and marking the wavelet basis corresponding to the maximum correlation coefficient CC as sigma.
And step nine, performing wavelet transformation on the spectral signal to be detected by using the wavelet basis sigma determined in the step eight, and extracting the mineral spectral characteristics.
The specific embodiment is as follows:
step 1, acquiring mineral spectrum data, measuring mineral spectrum through an ASD spectrometer, and recording a certain mineral spectrum curve obtained through measurement as Xi(lambda), where lambda is the number of the spectral band, the total number of lambda is 2151 in this example, i is the number for measuring the spectrum of the same mineral, and the total number of i measured in this example is 10.
And 2, denoising the mineral spectrum in the step 1 by using a mean value method, and recording the result as Z (lambda). For certain mineral spectrum X obtained by measurementi(lambda) taking an average value after summing according to corresponding wave bands, wherein the formula of denoising by the averaging method is as follows:
step 3, determining the wavelet cluster type to be selected and a series of wavelet bases contained in the wavelet cluster type, wherein the wavelet cluster type is not limited at all;
but by way of example, the wavelet clusters in the embodiment are selected from db, symlet and coiflet, the number of wavelet bases contained in the wavelet clusters can be adjusted according to requirements, and the wavelet series in the embodiment include db1, db2, db3, db4, db5, db6, db7, db8, db9 and db 10; symlet wavelet series comprises sym1, sym2, sym3, sym4, sym5, sym6, sym7, sym8, sym9, and sym 10; the coiflet wavelet series comprises coif1, coif2, coif3, coif4, coif5 and coif 6.
And 4, carrying out multi-scale one-dimensional discrete wavelet decomposition on the mineral spectrum signals in the step 2 by using the wavelet basis in the step 3 to obtain high-frequency detail coefficients and low-frequency approximate coefficients of different scales. In this embodiment, a wavedec function in Matlab is selected to perform one-dimensional discrete wavelet decomposition on the spectral signal Z (λ) obtained in step 2, the wavelet type is set as a series of wavelet bases determined in step 3, the number m of decomposition layers is set as 6, and after decomposition of each wavelet base, a high-frequency detail coefficient D of 6 scales can be obtainedi(i ═ 1,2,3,4,5,6) and low-frequency approximation coefficient ai(i＝1,2,3,4,5,6)。
Step 5, all the high-frequency detail coefficients D obtained in the step 4 are processedi(i-1, 2,3,4,5,6) soft thresholding, the result being denoted as Di' (i is 1,2,3,4,5,6), in this embodiment, the wthresh function in Matlab is selected for soft threshold processing.
Step 6, utilizing the highest scale low-frequency approximate coefficient A obtained in the step 46And step 5, performing soft threshold processing on each scale of high-frequency detail coefficient (D)1',D2',D3',D4',D5',D6') performing wavelet reconstruction to obtain a reconstructed signal S (lambda) after soft threshold denoising. In this embodiment, a waverec function in Matlab is selected for wavelet reconstruction, the wavelet base type is the same as the type set during one-dimensional discrete wavelet decomposition, and the decomposition coefficient used during reconstruction is [ a ]6,D6',D5',D4',D3',D2',D1']。
And 7, calculating a correlation coefficient CC between the reconstructed signal S (lambda) in the step 6 and the original mineral spectrum signal Z (lambda) in the step 2, wherein the calculation formula is as follows:
wherein cov represents a covariance operation.
And 8, sequencing the CCs calculated in the step 7, and marking the wavelet basis corresponding to the maximum CC as sigma, wherein the wavelet basis sigma corresponding to the maximum CC is db7 in the embodiment.
And 9, performing wavelet transformation on the spectral signal to be detected by using the wavelet base db7 determined in the step 8, and extracting the mineral spectral characteristics.
While the embodiments of the present invention have been described in detail, the present invention is not limited to the above-described examples, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (8)
1. A method for selecting wavelet base in mineral spectral feature extraction is characterized by comprising the following steps: the method comprises the following steps:
step one, acquiring mineral spectrum data;
secondly, denoising the mineral spectrum in the first step by a mean value method;
determining the category of the wavelet cluster to be selected and a series of wavelet bases contained in the wavelet cluster to be selected;
step four, performing multi-scale one-dimensional discrete wavelet decomposition on the mineral spectrum signals in the step two by using the wavelet basis in the step three to obtain high-frequency detail coefficients and low-frequency approximate coefficients of different scales;
step five, performing soft threshold processing on all the high-frequency detail coefficients obtained in the step four;
step six, performing wavelet reconstruction by using the high-frequency detail coefficient of each scale processed by the soft threshold in the step five and the highest-scale low-frequency approximate coefficient obtained in the step four to obtain a reconstructed signal subjected to soft threshold noise reduction;
step seven, calculating the correlation coefficient of the reconstructed signal in the step six and the mineral spectrum original signal in the step two;
step eight, determining a wavelet basis corresponding to the maximum correlation coefficient in the step seven;
and step nine, performing wavelet transformation on the spectral signal to be detected by using the wavelet basis determined in the step eight, and extracting the mineral spectral characteristics.
2. A method of selecting wavelet basis in the spectral feature extraction of minerals according to claim 1, characterized by: the first step further comprises: the measured spectrum curve of a certain mineral is recorded as Xi(lambda), wherein lambda is the serial number of the spectral band, and i is the serial number of the mineral spectrum measured multiple times.
3. A method of selecting wavelet basis in the spectral feature extraction of minerals according to claim 2, characterized by: the second step further comprises: for certain mineral spectral curve X obtained by measurementi(lambda), summing according to corresponding wave bands, and then taking an average value, and recording the result as Z (lambda); assuming that n spectral measurements are performed on the mineral, the formula of mean denoising is as follows (1):
4. a method of selecting wavelet basis in the spectral feature extraction of minerals according to claim 3, characterized by: the fourth step further comprises: the wavelet basis functions are noted
Using wavelet bases
Performing m-layer one-dimensional discrete wavelet decomposition on the mineral spectrum signal Z (lambda) to obtain high-frequency detail coefficients D with different scalesi(i ═ 1,2, …, m) and low frequency approximation coefficient ai(i＝1,2,…,m)。
5. A method for selecting wavelet basis in the extraction of spectral features of minerals according to claim 4, characterized by: the fifth step further comprises: all the high-frequency detail coefficients D obtained in the step fouri(i 1,2, …, m) was soft thresholded, the result being denoted as Di'(i＝1,2,…,m)。
6. A method for selecting wavelet basis in the extraction of spectral features of minerals according to claim 5, wherein; the sixth step further comprises: utilizing the high-frequency detail coefficient D of each scale after the five soft threshold processing of the stepsi' (i is 1,2, …, m) and the highest scale low frequency approximation coefficient A obtained in step fourmAnd performing wavelet reconstruction to obtain a reconstructed signal S (lambda) subjected to soft threshold denoising.
7. A method for selecting wavelet basis in the extraction of spectral features of minerals according to claim 6, wherein: the seventh step further comprises: and (3) calculating a correlation coefficient CC of the reconstructed signal S (lambda) in the sixth step and the original mineral spectrum signal Z (lambda) in the second step, wherein the calculation formula is as follows (2):
wherein cov represents a covariance operation.
8. The method for selecting wavelet base in mineral spectral feature extraction according to claim 7, wherein: the eighth step further comprises: and sequencing the correlation coefficients CC calculated in the seventh step, and marking the wavelet basis corresponding to the maximum CC as sigma.
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| CN113592743A (en) * | 2021-08-11 | 2021-11-02 | 北华航天工业学院 | Spectrum high-frequency information and low-frequency information separation and coupling method based on complex wavelet transformation |
| CN113992237A (en) * | 2021-10-27 | 2022-01-28 | 天津光电通信技术有限公司 | Wavelet self-adaptive threshold signal-noise separation method and device based on 5G pulse forming |
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| CN113592743A (en) * | 2021-08-11 | 2021-11-02 | 北华航天工业学院 | Spectrum high-frequency information and low-frequency information separation and coupling method based on complex wavelet transformation |
| CN113592743B (en) * | 2021-08-11 | 2024-01-23 | 北华航天工业学院 | Spectral high-frequency information and low-frequency information separation and coupling method based on complex wavelet transformation |
| CN113992237A (en) * | 2021-10-27 | 2022-01-28 | 天津光电通信技术有限公司 | Wavelet self-adaptive threshold signal-noise separation method and device based on 5G pulse forming |
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